Search for the Stolen Remnant Core
It's possible there are too many things in this game that can be called 'Remnant Core.'
Regardless, this triggers automatically at the end of Investigate Remnant Derelict. Summon the NOMAD and follow Suvi's navpoint to a cluster of crates, next to a Remant ruin, overrun with Fiends and other exotic fauna.
If the idea of taking on two Fiends is too much for your party the moment, you might let the creatures fight amongst themselves for a while. Otherwise kiting the big guys around the sand here isn't too hard- their only distance attack is slow and inaccurate. When everything's dead, scan the small crate in the center of all those big crates for your next lead.
Your next navpoint is crashed shuttle (sure seems to happen a lot in Andromeda). There is a container to loot and many things to scan. Listen to SAM when she comes online for a chat, then snag the datapad in the center of the wreckage.
Follow your last navpoint to the cave at the lowest level of the Flophouse area (You don't have to clear out the whole Flophouse to access the cave).
Inside the cave you'll find a small complex filled with Raiders, Sharpshooters, adhi, and Berserkers.
Your main strategy is not to get attacked from behind by the latter two enemies while peering through a scope at the former. There's plenty of cover here, so you can always dash to a new spot if your current position is compromised. When the enemies are all dead, drop down to the lowest level to loot some containers, and then recover the Drive Core (which looks an awful lot like two data cores tilted head-to-head).
Interface with the Drive Core to claim it, then head back to New Tuchanka to sort things out. Talk to Morda, and reveal Strux's treachery. You'll be treated to some krogan fisticuffs, but then you have a choice to make.
You can keep the uber-powerful core for yourself, or gift it to the krogan. If the former, you cannot establish an outpost on Elaaden, which makes a number of quests impossible to complete. If the latter, you make peace with New Tuchanka, you get to establish a colony here, and all is well as it is likely to be.
Making this choice completes the quest.